We present a theoretical calculation of the atomic and electronic structure of β-SiC and its non-polar (110) surface using the full potential linear augmented plane wave (FPLAPW) approach. The calculated lattice constant and bulk modulus of p-SiC crystal are in excellent agreement with experimental data. The atomic and electronic structure of β-SiC(110) surface has been calculated by employing the slab and supercell model. It is found that the surface is characterized by a top-layer bond-length-contracting rotation relaxation in which the Si-surface atom moves closer towards the substrate while the C-surface atom moves outward. This relaxation is analogous to that of Ⅲ-Ⅴ semiconductor surface. The driving mechanism for this atomic rearrangement is that the Si atom tends to a planar sp2-like bonding situation with its three N neighbors and the N atom tends to a p3-like bonding with its three Si neighbors. Furthermore, surface relaxation induces the change from metallic to semiconducting